Cryptographic protocols on real hyperelliptic curves

We present public-key cryptographic protocols for key exchange, digital signatures, and encryption whose security is based on the presumed intractability of solving the principal ideal problem, or equivalently, the distance problem, in the real model of a hyperelliptic curve. Our protocols represent a significant improvement over existing protocols using real hyperelliptic curves. Theoretical analysis and numerical experiments indicate that they are comparable to the imaginary model in terms of efficiency, and hold much more promise for practical applications than previously believed.